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The world of advanced baseball statistics can be an intimidating place for those of us who slept our way through advanced algebra or haven't been a follower of the Bill James revolution from the beginning. 

Still, that doesn't mean that we should feel left out when it comes to another way of understanding and appreciating the game we all love. With that in mind, BLS stat doctor Alex Remington will explore a new advanced statistic each week during the offseason, providing a simple primer for the uninitiated.

Today's statistic: WPA

What it stands for: Win Probability Added. As Hardball Times's Dave Studeman has written, it's gone by a lot of different names. "Player Win Averages," "Player Game Percentage," "Win Expectancy," "Player's Win Value," etc. But WPA is the the most common name for it these days.

How they calculate WPA: Though the arithmetic can be a mother, Win Probability Added is one of the easiest of all the advanced stats to explain. Put simply, it's a measure of how much any game event contributes to the eventual outcome of the game, win or loss.

Or, as Fangraphs' David Appelman writes, "WPA is the difference in win expectancy (WE) between the start of the play and the end of the play." (For those of you who remember calculus, this means it's a marginal measure — it measures the difference in probability between two states. Feel free to use a Greek Delta symbol in your mind.)

So how much does that single in the second inning make it likelier that team will win? How much likelier is the win after the setup man got three crucial outs in the eighth?

To find out, we have to consult a win expectancy chart -- or let baseball-reference.com or Fangraphs do the work for us. There's a WPA calculator spreadsheet here that has all the necessary math and allows you to plug in values on your own. (Tom Tango explains the calculations on a win expectancy chart here. Basically, it involves running simulations on every conceivable game context — "from a score differential of minus 30 runs to plus 30 runs, from the first inning to the thirtieth inning, from bases empty to bases loaded, and for zero, one, and two outs." Whew.)

What WPA is good for: WPA is good for telling you who deserves the game ball. WPA analysis is also good for storytelling.  It gives you a statistical evidence that this was the turning point of the game, the most important play. WPA is a new-school stat in old-school garb — it tells you exactly what happened, and exactly how important it was.

Unlike context-neutral stats (FIP, wOBA, WAR, etc.) which ignore whether there were men on base or whether it was a close game, WPA specifically measures how much that player contributed to the team's likelihood of winning that day.

How WPA works: WPA  quantifies the contextual value of any given play — a late home run in a close game is worth more than the third solo shot in a back-to-back-to-back series. It doesn't penalize a player if the team lost the game despite his best efforts, exactly — but it does examine the game in the context of what happened, rather than what "should" have happened if not for the statistical noise of random chance. Fangraphs' live WPA scoreboards provide a perfect illustration of WPA in action. They show you the turning points of the game and the exact heroes and goats.

In the last game of the World Series, which the above link and graph to the right shows, Matsui's first homer was a major turning point in the game. It broke the scoreless tie and gave the Yankees a lead they'd never relinquish. It had a WPA of .150, the highest value of any offensive play in the game. The lowest WPA was a -0.66 for Alex Rodriguez's(notes) bases-loaded strikeout in the third, when it looked like the Yankees might squander an early chance to blow the game open. Then Matsui hit a two-run single — the second-biggest play of the game, with a WPA of .143 — and put the game safely in Yankee hands.

When WPA doesn't work: As Tom Tango says, "WPA is not a way to evaluate the talent of a player." It's entirely context-specific. In other words, it's great for game analysis, but less great for player analysis. It's like the percentages they show on World Series of Poker broadcasts: it just tells you the percentages of victory during that hand, not the talent levels of the poker players involved.

Why we care about WPA: It's such a great stat that  it's been exported to other sports. Here's a real-time WPA scoreboard for the NFL, NBA, and NHL, courtesy of Advanced NFL Stats. Like I said, it's a real storytelling stat. Even more than a box score, a WPA graph shows you each shift of the momentum of the game, every moment of agony and ecstasy when the pendulum swung in the other direction.

As with all measures of Win Expectancy, it can also give you a good idea of situational strategy. In almost all situations — but not entirely all — intentional walks and non-pitcher sacrifice bunts result in a negative WPA, but in certain situations they don't. (In 2002, Tango introduced a chart of when a team should intentionally walk Barry Bonds(notes).) WPA takes the old colloquialisms about "playing the percentages" in baseball and makes it a reality. There actually are percentages for every play in baseball.

Thanks to WPA, we can see what they are.

Next week's lesson: WAR

Previous lessons: BABIP, OPS+, FIP, wOBA

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